IK on eyeball does not move how I tell it to - Resolved
For the specific eye problem, you should not choose the eye bone as the parent of the eye handle bone, also give your eye bone a Track To constraint with the eye handle as bone target. You have other problems like you should apply your Mirror modifier, only the eye bone should influence the eye mesh, the control bones need to have their Deform option disabled, your IK handles should only have the root bone as parent, in Edit mode recalculate the bones roll with ctrlN, etc...